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PDF-2GAUTAMBHARALIisolated,degenerateCRsingularity.GivenacompactsubsetKCn PDF document

z FzwherezwareholomorphiccoordinatesonC2FisasmoothfunctionsatisfyingFzojzjkasz0andk2AssumethatShasanisolatedCRsingularityattheoriginLetuswriteX kC z z Ck0zkC0k zkzC0k

z +F(z);where(z;w)areholomorphiccoordinatesonC2 FisasmoothfunctionsatisfyingF(z)=o(jzjk)asz!0 andk2.AssumethatShasanisolatedCRsingularityattheorigin.LetuswriteX + =kC ; z z =Ck;0zk+C0;k zk+(z);C0;k

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